Alan and Bob are trying to figure out two numbers. They know that both numbers are integers between 1 and 100 (but not 1 or 100). Alan knows the product of the numbers, and Bob knows the sum. Their conversation goes as follows:
Alan: I can't tell what the two numbers are.
Bob: I knew you couldn't.
Alan: Ok, now I know the numbers.
Bob: Now I know them, too.
What are the two numbers?